Question

The sum of digit of a two digit number is 11. If the digit at ten's place is increased by 5 and the digit at unit place is decreased by 5, the digits of the number are found to be reversed. Find the original number.

Answer 1

Let x be the number at the ten's place.
and y be the number at the unit's place.
So, the number is 10x + y.

The sum of digit of a two digit number is 11.
⇒ x + y = 11                             ...(1)

lf the digit at ten's place is ineased by 5 and the digit at unit place is decreased by 5,
the digits of the number are found to be reversed.
⇒  10( x + 5 ) + ( y - 5 ) = 10y + x
⇒  9x - 9y = -45
⇒  x - y = -5                              ...(2)

Subtracting equation (1) from equation (2), we get :
      x - y = - 5
-    x + y = 11  
     -   -      -     
         - 2y = - 16
⇒ y = 8

Substituting y = 8 in equation (1), we get
x + 8 = 11
⇒ x = 3
∴ The number is 10x + y = 10(3) + 8 = 38.